Theorems · Theorem · category theory
CategoryTheory.MonObj.one_mul
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} (X : C)
[self : CategoryTheory.MonObj X],
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.MonObj.one X)
CategoryTheory.MonObj.mul =
(CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom- Defined in
- Mathlib.CategoryTheory.Monoidal.Mon
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.MonObj
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
- CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
- CategoryTheory.MonObj.mulstatement · cited by 230
- CategoryTheory.MonObjstatement and proof · cited by 199
- CategoryTheory.MonObj.onestatement · cited by 189
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.MonObj.lift_comp_one_leftproof · cited by 4
- CategoryTheory.MonObj.extproof · cited by 3
- Bimod.LeftUnitorBimod.hom_inv_idproof · cited by 2
- CategoryTheory.HopfObj.mul_antipode₂proof · cited by 1
- CategoryTheory.MonObj.one_mul_homproof · cited by 1
- CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mulproof · cited by 1
- CategoryTheory.MonObj.one_mul_assocproof · cited by 0
- CategoryTheory.MonObj.Mon_tensor_one_mulproof · cited by 0
- CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mulproof · cited by 0
- Bimod.id_whiskerLeft_bimodproof · cited by 0